Problem: ${\sqrt[3]{864} = \text{?}}$
Explanation: $\sqrt[3]{864}$ is the number that, when multiplied by itself three times, equals $864$ First break down $864$ into its prime factorization and look for factors that appear three times. So the prime factorization of $864$ is $2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$ Notice that we can rearrange the factors like so: $864 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 = (2\times 2\times 2) \times (3\times 3\times 3) \times 2\times 2$ So $\sqrt[3]{864} = \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{3\times 3\times 3} \times \sqrt[3]{2\times 2}$ $\sqrt[3]{864} = 2\times 3 \times \sqrt[3]{2\times 2}$ $\sqrt[3]{864} = 6 \sqrt[3]{4}$